Phase relationships

Basic characteristics of soils

For soil D the liquid limit is obtained from Figure 1.14, in which fall-cone penetration is plotted against water content. The percentage water content, to the nearest integer, corre- sponding to a penetration of 20 mm is the liquid limit, and is 42%. The plastic limit is the average of the two percentage water contents, again to the nearest integer, i.e. 24%. The plasticity index is the difference between the liquid and plastic limits, i.e. 18%.

Soil A consists of 100% coarse material (76% gravel size; 24% sand size) and is classified as GW: well-graded, very sandy GRAVEL.

Soil B consists of 97% coarse material (95% sand size; 2% gravel size) and 3% fines. It is classified as SPu: uniform, slightly silty, medium SAND.

Soil C comprises 66% coarse material (41% gravel size; 25% sand size) and 34% fines (w_L = 26, I_P = 9, plotting in the CL zone on the plasticity chart). The classification is GCL:

very clayey GRAVEL (clay of low plasticity). This is a till, a glacial deposit having a large range of particle sizes.

Soil D contains 95% fine material: the liquid limit is 42 and the plasticity index is 18, plotting just above the A-line in the CI zone on the plasticity chart. The classification is thus CI: CLAY of intermediate plasticity.

three-phase, being composed of solid soil particles, pore water and pore air. The components of a soil can be represented by a phase diagram as shown in Figure 1.15(a), from which the following relationships are defined.

The water content (w), or moisture content (m), is the ratio of the mass of water to the mass of solids in the soil, i.e.

w M

= M^w

s

(1.6) The water content is determined by weighing a sample of the soil and then drying the sample in an oven at a temperature of 105–110°C and re-weighing. Drying should continue until the dif- ferences between successive weighings at four-hourly intervals are not greater than 0.1% of the original mass of the sample. A drying period of 24 h is normally adequate for most soils.

The degree of saturation or saturation ratio (S_r) is the ratio of the volume of water to the total volume of void space, i.e.

S V

r Vw v

= (1.7)

The saturation ratio can range between the limits of zero for a completely dry soil and one (or 100%) for a fully saturated soil.

The void ratio (e) is the ratio of the volume of voids to the volume of solids, i.e.

e V

= V^v

s

(1.8) The porosity (n) is the ratio of the volume of voids to the total volume of the soil, i.e.

n V

= V^v (1.9)

As V = V_v+Vs, void ratio and porosity are interrelated as follows:

e n

= n -

1 (1.10)

Figure 1.15 Phase diagrams.

Basic characteristics of soils

n e

= e

1+ (1.11)

The specific volume (v) is the total volume of soil which contains a unit volume of solids, i.e.

v V

V e

= = +

s

1 (1.12)

The air content or air voids (A) is the ratio of the volume of air to the total volume of the soil, i.e.

A V

= V^a (1.13)

The bulk density or mass density (ρ) of a soil is the ratio of the total mass to the total volume, i.e.

r= M

V (1.14)

Convenient units for density are kg/m³ or Mg/m³. The density of water (1000 kg/m³ or 1.00 Mg/

m³) is denoted by ρw.

The specific gravity of the soil particles (G_s) is given by

G M

s V s

s w s w

= =

r r

r (1.15)

where ρs is the particle density.

From the definition of void ratio, if the volume of solids is 1 unit then the volume of voids is e units. The mass of solids is then G_sρw and, from the definition of water content, the mass of water is wG_sρw. The volume of water is thus wG_s. These volumes and masses are represented in Figure 1.15(b). From this figure, the following relationships can then be obtained.

The degree of saturation (definition in Equation 1.7) is S V

V

wG

r w e

v

= = s (1.16)

The air content is the proportion of the total volume occupied by air, i.e.

A V V

e wG

= = - e +

a s

1 (1.17)

or, from Equations 1.11 and 1.16,

A n=

(

¹-S^r

)

^(1.18)

From Equation 1.14, the bulk density of a soil is:

r= =

(

+

)

r + M

V

G w

e

s 1 w

1 (1.19)

or, from Equation 1.16,

r= + r

+ G S e

e

s r

1 w (1.20)

Equation 1.20 holds true for any soil. Two special cases that commonly occur, however, are when the soil is fully saturated with either water or air. For a fully saturated soil S_r = 1, giving:

rsat s r

= + w

+ G e

1 e (1.21)

For a completely dry soil (S_r = 0):

rd s r

= w

+ G

1 e (1.22)

The unit weight or weight density (γ) of a soil is the ratio of the total weight (Mg) to the total volume, i.e.

g= Mg = r V g

Multiplying Equations 1.19 and 1.20 by g then gives g = G^s w gw

e (1 ) 1

+

+ (1.19a)

g = G^s S e^r gw

e +

1+ (1.20a)

where γw is the unit weight of water. Convenient units are kN/m³, the unit weight of water being 9.81kN/m³ (or 10.0kN/m³ in the case of sea water). Unit weight is usually used in preference to density as it can be more directly used to calculate (total and effective) stresses within the ground (see Chapter 3).

In the case of sands and gravels the relative density (I_D) is used to express the relationship between the in-situ void ratio or void ratio of a sample (e), and the limiting values e_max and e_min representing the loosest and densest possible soil packing states respectively. The relative density is defined as

I e e

e e

D = -

-

max max min

(1.23) Thus, the relative density of a soil in its densest possible state (e = e_min) is 1 (or 100%) and in its loosest possible state (e = e_max) is 0.

The maximum density is determined by compacting a sample underwater in a mould, using a circular steel tamper attached to a vibrating hammer: a 1-l mould is used for sands and a 2.3-l mould for gravels. The soil from the mould is then dried in an oven, enabling the dry density to be determined. The minimum dry density can be determined by one of the following procedures.

In the case of sands, a 1-l measuring cylinder is partially filled with a dry sample of mass 1000 g and the top of the cylinder closed with a rubber stopper. The minimum density is achieved by shaking and inverting the cylinder several times, the resulting volume being read from the gradu- ations on the cylinder. In the case of gravels and sandy gravels, a sample is poured from a height of about 0.5 m into a 2.3-l mould and the resulting dry density determined. Full details of the above tests are given in BS 1377, Part 4 (1990). Void ratio can be calculated from a value of dry

Basic characteristics of soils

density using Equation 1.22. However, the density index can be calculated directly from the maximum, minimum and in-situ values of dry density, avoiding the need to know the value of G_s (see Problem 1.5).

Table 1.6 summarises indicative values of useful soil continuum properties for a variety of soil types, including unit weights in the fully saturated condition (γsat), values of emax and emin

(for coarse-grained soils only) and typical natural water contents. These values may be useful for checking the results of laboratory tests described in this chapter, and for making initial esti- mates of parameters before such tests have been undertaken. They therefore support, rather than replace, careful determination of these properties in the laboratory.

Example 1.2

In its natural condition, a soil sample has a mass of 2290 g and a volume of 1.15 × 10^–3 m³. After being completely dried in an oven, the mass of the sample is 2035 g. The value of G_s for the soil is 2.68. Determine the bulk density, unit weight, water content, void ratio, porosity, degree of saturation and air content.

Solution

Bulk density,r= = kg/m Mg/m

´ ^- =

( )

M V

2 290

1 15 10. ₃ 1990 ³ 1 99 ³

. .

Unit weight, 500 N/m

kN/m

g= = ´ =

= Mg

V 1990 9 8 19 19 5

3

3

. .

Water content, ^w or 12.5%

s

w M

= M =2290 2035- = 2035 0 125. From Equation 1.19,

Table 1.6 Typical continuum soil properties (data collated from Bowles, 1979 and Barnes, 2010)

Soil type γsat (kN/m³) e_max e_min w^a (%)

Sand & gravel 16–22 0.80–0.44^b 0.50–0.20^b 0–25

Silt 16–20 0.86–0.68 0.68–0.49 10–30

Stiff clay/Glacial till^c 19–23 N/A N/A 10–20/20–40

Soft clay 17–20 N/A N/A 20–40/50–90

Peat (organic) 10–14 N/A N/A > 100

a Water content ranges for clays are given for low plasticity/high plasticity

b e_max and e_min ranges will be higher if there are significant fines (e.g. clayey or silty sands)

c Glacial tills are typically γsat ≈21 kN/m³, w≈10%

Void ratio, = e Gs( w) w

. .

.

1 1

2 68 1 125 1000 1990 1 1 5

+ -

=æ ´ ´

èç ö

ø÷-

=

r r

22 1 0 52

-

= .

Porosity,n e or 34%

= e

+ = =

1

0 52 1 52. 0 34

. .

Degree of saturation,Sr wGs or 64.5%

= e =0 125 2 68´ = 0 52 0 645

. .

. .

Air content,

or 12.1%

A n= −Sr = ×

=

( ) . .

.

1 0 34 0 355 0 121

Summary

1 Soil is a particulate material formed of weathered rock. The particles may be sin- gle grains in a wide range of sizes (from boulders to silt), or clay minerals (colloidal in size). Soil is typically formed from a mixture of such particles, and the presence of clay minerals may significantly alter the mechanical properties of the soil.

2 Soils may be described and classified by their particle size distribution. Fine soils consisting of mainly small particles (e.g. clays and silts) typically exhibit plastic behaviour (e.g. cohesion) which may be defined by the plasticity and liquidity indices. Coarse-grained soils generally do not exhibit plastic behaviour.

3 At the level of the macro-fabric, all soils may be idealised as a three-phase con- tinuum, the phases being solid particles, water and air. The relative proportions of these phases are controlled by the closeness of particle packing, described by the voids ratio (e), water content (w) and saturation ratio (S_r).

Problems

1.1 The results of particle size analyses and, where appropriate, limit tests on samples of four soils are given in Table 1.7. Allot group symbols and give main and qualifying terms appro- priate for each soil.

1.2 A soil has a bulk density of 1.91 Mg/m³ and a water content of 9.5%. The value of G_s is 2.70.

Calculate the void ratio and degree of saturation of the soil. What would be the values of density and water content if the soil were fully saturated at the same void ratio?

Basic characteristics of soils

1.3 Calculate the dry unit weight and the saturated unit weight of a soil having a void ratio of 0.70 and a value of G_s of 2.72. Calculate also the unit weight and water content at a degree of saturation of 75%.

1.4 A soil specimen is 38 mm in diameter and 76 mm long, and in its natural condition weighs 168.0 g. When dried completely in an oven, the specimen weighs 130.5 g. The value of G_s is 2.73. What is the degree of saturation of the specimen?

1.5 The in-situ dry density of a sand is 1.72 Mg/m³. The maximum and minimum dry densities, determined by standard laboratory tests, are 1.81 and 1.54 Mg/m³, respectively. Determine the relative density of the sand.

References

ASTM D2487-17 (2017) Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System), American Society for Testing and Materials, West Conshohocken, PA.

ASTM D4318-17 (2017) Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils, American Society for Testing and Materials, West Conshohocken, PA.

ASTM D6913-17 (2017) Standard Test Methods for Particle Size Distribution (Gradation) of Soils Using Sieve Analysis, American Society for Testing and Materials, West Conshohocken, PA.

Barnes, G.E. (2009) An apparatus for the plastic limit and workability of soils, Proceedings ICE—Geotechnical Engineering, 162(3), 175–185.

Barnes, G.E. (2010) Soil Mechanics: Principles and Practice, Palgrave Macmillan, London.

Bowles, J.E. (1979) Physical and Geotechnical Properties of Soils, McGraw Hill Inc.

British Standard 1377-4 (1990) Methods of Test for Soils for Civil Engineering Purposes:

Compaction-Related Tests, British Standards Institution, London.

Table 1.7 Problem 1.1

BS sieve Particle size Percentage smaller

Soil I Soil J Soil K Soil L

63 mm

20 mm 100

6.3 mm 94 100

2 mm 69 98

600 μm 32 88 100

212 μm 13 67 95 100

63 μm 2 37 73 99

0.020 mm 22 46 88

0.006 mm 11 25 71

0.002 mm 4 13 58

Liquid limit Non-plastic 32 78

Plastic limit 24 31

British Standard BS EN ISO 14688-1 (2018) Geotechnical Investigation and Testing – Identification and Classification of Soil. Identification and Description (ISO 14688-1: 2017), British Standards Institution, London.

British Standard BS EN ISO 14688-2 (2018) Geotechnical Investigation and Testing – Identification and Classification of Soil. Principles for a Classification (ISO 14688-2: 2017), British Standards Institution, London.

British Standard BS EN ISO 17892-4 (2016) Geotechnical Investigation and Testing – Laboratory Testing of Soil, Part 4: Determination of Particle Size Distribution, British Standards Institution, London.

British Standard 5930 (2015) Code of Practice for Site Investigations, British Standards Institution, London.

CEN ISO/TS 14688 (2002) Geotechnical Investigation and Testing—Laboratory Testing of Soil, International Organisation for Standardisation, Geneva.

CEN ISO/TS 17892 (2004) Geotechnical Investigation and Testing—Laboratory Testing of Soil, International Organisation for Standardisation, Geneva.

Day, R.W. (2001) Soil Testing Manual, McGraw Hill, New York, NY.

Mitchell, J.K. and Soga, K. (2005) Fundamentals of Soil Behaviour (3rd edn), John Wiley &

Sons, New York, NY.

Sivakumar, V., Glynn, D., Cairns, P. and Black, J.A. (2009) A new method of measuring plastic limit of fine materials, Géotechnique, 59(10), 813–823.

Waltham, A.C. (2009) Foundations of Engineering Geology (3rd edn), CRC Press, Abingdon, Oxfordshire.

White, D.J. (2003) PSD measurement using the single particle optical sizing (SPOS) method, Géotechnique, 53(3), 317–326.

Further reading

Collins, K. and McGown, A. (1974) The form and function of microfabric features in a variety of natural soils, Géotechnique, 24(2), 223–254.

Provides further information on the structures formed by soil particles under different deposi- tional regimes.

Grim, R.E. (1962) Clay Mineralogy, McGraw-Hill, New York, NY.

Further detail about clay mineralogy in terms of its basic chemistry.

Rowe, P.W. (1972) The relevance of soil fabric to site investigation practice, Géotechnique, 22(2), 195–300.

Presents 35 case studies demonstrating how the depositional/geological history of the soil depos- its influences the selection of laboratory tests and their interpretation, and the consequences for geotechnical constructions. Also includes a number of photographs showing a range of different soil types and fabric features to aid interpretation.

Henkel, D.J. (1982) Geology, geomorphology and geotechnics, Géotechnique, 32(3), 175–194.

Presents a series of case studies demonstrating the importance of engineering geology and geo- morphological observations in geotechnical engineering.

For further student and instructor resources for this chapter, please visit the Companion Website at www.routledge.com/cw/craig

Seepage

Chapter 2

Seepage

Learning outcomes

After working through the material in this chapter, you should be able to:

1 Determine the permeability of soils using the results of both laboratory tests and in-situ tests conducted in the field (Sections 2.1 and 2.2);

2 Understand how groundwater flows for a wide range of ground conditions, and determine seepage quantities and pore pressures within the ground (Sections 2.3–2.7);

3 Use computer-based tools for accurately and efficiently solving larger/more com- plex seepage problems (Section 2.8);

4 Assess seepage through and beneath earthen dams, and understand the design features/remedial methods which may be used to control this (Sections 2.9–2.10).